Abstract
The Zermelo problem studies the trajectories which minimize the time in the presence of a wind or current, as for example when we consider a sailboat in the sea or a ship in a river. The solution is given by Finsler metrics whose indicatrix is the translation by the wind vector of the indicatrix of the background metric. When the wind is strong, the origin of coordinates can be away from the indicatrix and then it defines two conic Finsler metrics. In particular, if the background metric is a Riemannian metric, with the translation we will obtain a Randers or a Kropina metric. We show that the flag curvature is preserved when the indicatrix is translated with a Killing field, using the dual metric, which is a Hamiltonian function in the cotangent bundle. Moreover, these metrics also have applications to spacetimes endowed with a Killing field (not necessarily timelike). - Joint work with Henrique Vitório -
